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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 131r, page id 00068195:0261
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ac + b
b
e
bd +c
Ebc sa cd cd
bi ac+b
cd vc Xd
acd + bd + bc
bcd
In tali ergo casu, cum fractiones summendo sunt, q ita comparatae, ut
se nommator praecedentis sit numerator antecdentis, fiat fractio, cujus
nominator, sit factus ex omnibus terminis demtoprimo numerator compositus
ex tot terminis quot sunt fractiones, et quaelibet pars ex omnibus terminis ita
it
ita componato, ita ut prima constet ex omnibus terminis, demto se secundo, secunda
ex omnibus terminis demto tertio, et ita porro. ita terninus pri pars prima numeralori
differet a nominatores quod loco termini 2di, habet primum, (quo nominator caret)
pars 2da Ao, quod loco termini 3tii habebit idum C.
dam ut talia: acd +bd + bc  4 + h +E
d
bcd
breoder symnes ita orinor agendum erit: differentia imer acd+  b
uud sic potius; nominator habet ses demito primo, primus numerator habet oes
demto, ido reliquinumeratores habent suum terminum bis, et carent praxime
ante adentet proxime sequente. differentia inter acd-
summam ita investigabimus: acd + b d = ac + bd
bd + bc = bd +E b
Hini apparet si b. sit media proportionalis inter a et c. vel C inbib et d. tunc
ad summam inundam, tantum primum terminum multiplicari possi per numerum termonorum
et facto velut numeratori subscribi posse nominatorem factum ex omnibus terminis
dento primo v.g. acd + b d + b facilius perveniri posse, quia ac = b et bd=
1 2. 4. 8. 16. et sit  q l B ibi mendi poterd oes temminos esse
Quid verd si temini siil Arithmeliae proportionales, ita stabit:
a + 2aX
1+37
act, t a a atir, 4 at or  atr, atn aror, f an acin atx
a + 2 X + 3aX +6 aX
a lax + ran = 3a X + 3X  6aX =
= a2+ 3X +5AX + 7 ax
atx a + 2X a+ 3X. (bd) arxat
Ar  + = +  + . sintque a. b. c. d. e progressionis arihm etiae.
a +  = 4t +b (B huc aequita ulilis observatu ad reduchines) i 
B+C
ee
a +X.
a +b, 1 ab + bc + ac  + - abe + abd 1acd +bed. Et (hoc schema unversalcest
ab NC abc.
abcd
in omnium fractionum additione, in quibus Numerator Unitas. Cum jam numeri su pr termni
sint progressionis Arithmetuae, sunto a = a. b- a + IX c = a + x d = a + 3x ex
1+ = = a + b = a + a +X 2a +X
ab
a aIX ara
+
1 E
L. abtbetac. arax + a + Er FSax F a trax (3 a 1 6ax 1 2
abc
quod si jam X- a. erit 3a X Ha et si a = 1. erit 1
ad + 3a X F 2aX 9 a +3aX134
math. X1B 2 131
ac + b +, bd + c acd +bcd + +b d tbC-
cd
DCd
acd +bd + bc
bca
Ca a a +2K =
a + 2aX
abc a aFL atEs
= a + aX  a + 2X.
+ a X + 24
F ax
30